I actually posted this same idea a month ago and it was met with a similar reception. I agree with the OP that shields should have their difficulty strength based. Shield skill on the other hand can remain agility based as the skill is a pseudo weapon proficiency category.
You would see the evolution of utility shieldmen who have high strength but lack shield skill; they would take board and huscarl shields for coverage against ranged fire, but be slow in their blocking with the heavy shields. There would also be skilled shieldmen with lower strength and high shield skill who take bucklers and smaller shields. No longer would bucklers only be available to the highest levels, which is currently incredibly stupid imo. Difficulty and gold price would not be so highly correlated as well hopefully (high difficulty/low gold price, low difficulty/high gold price, etc.).
The reason this idea would create unbalanced builds is due mostly to the speed at which you can backpeddle, rotate the character, and the benefits of strength per point. These are really problems with the game as a whole, so the idea isn't bad in itself, but rather because the game has some unrealistic mechanics already. Perhaps with wpe the idea is possible.